Critical analysis of the response function in low-dimensional materials.

Area of Science:

• Condensed matter physics
• Materials science
• Computational physics

Background:

• Sharp peaks in the static dielectric response function often indicate charge or spin instabilities in materials.
• A common misconception is that Fermi surface (FS) nesting alone guarantees these peaks, similar to 1D systems.
• Response function matrix elements are frequently simplified to unity, neglecting their impact.

Purpose of the Study:

• To investigate the role of Fermi surface (FS) nesting and matrix elements in predicting material instabilities.
• To challenge the assumption that FS nesting alone is sufficient for identifying instabilities.
• To demonstrate the necessity of calculating full response functions.

Main Methods:

• Utilized density functional theory (DFT) for calculations.
• Employed model systems and real materials for analysis.
• Explicitly included and analyzed response function matrix elements.

Main Results:

• Predictions based solely on FS nesting and constant matrix elements lead to erroneous conclusions.
• The inclusion of matrix elements significantly alters the response function's structure.
• For systems beyond one dimension, matrix elements tend to diminish the peak structures observed with constant matrix elements.

Conclusions:

• Fermi surface nesting is not a reliable sole predictor of instabilities.
• Response function matrix elements are critical and cannot be universally set to unity.
• Accurate prediction of instabilities in novel materials necessitates the calculation of the complete response function, including matrix elements.